System and method for performing process model calibration in a virtual semiconductor device fabrication environment

ABSTRACT

A virtual fabrication environment for semiconductor device fabrication that includes an analytics module for performing key parameter identification, process model calibration and variability analysis is discussed.

RELATED APPLICATIONS

This application is a continuation application of U.S. patentapplication Ser. No. 16/010,537, filed Jun. 18, 2018, entitled “Systemand Method for Key Parameter Identification, Process Model Calibrationand Variability Analysis in a Virtual Semiconductor Device FabricationEnvironment which claims priority to, and the benefit of, U.S.Provisional Patent Application No. 62/521,506, entitled “System andMethod for Analyzing Process Variation in a Virtual FabricationEnvironment For Improved Process Integration”, filed Jun. 18, 2017, andU.S. Provisional Patent Application No. 62/631,022, entitled “System andMethod for Process Model Calibration in a Virtual FabricationEnvironment”, filed Feb. 15, 2018, the contents of all of theabove-referenced applications incorporated herein by reference in theirentirety.

BACKGROUND

Integrated circuits (ICs) implement a myriad of capabilities of modernelectronic devices. To make the development of ICs more efficient, asemiconductor manufacturer will periodically develop a commonfabrication process or “technology” to be used for production of itsintegrated circuits (for ease of explanation the term “technology” maybe used herein to refer to a fabrication process for a semiconductordevice structure that is being developed).

Semiconductor development organizations at integrated devicemanufacturers (IDMs) and independent foundries spend significantresources developing the integrated sequence of process operations usedto fabricate the chips ((ICs) they sell from wafers (“wafers” are thinslices of semiconductor material, frequently, but not always, composedof silicon crystal). A large portion of the resources is spent onfabricating experimental wafers and associated measurement, metrology(“metrology” refers to specialized types of measurements conducted inthe semiconductor industry) and characterization structures, all for thepurpose of ensuring that the integrated process produces the desiredsemiconductor device structures. These experimental wafers are used in atrial-and-error scheme to develop individual processes for thefabrication of a device structure and also to develop the total,integrated process flow. Due to the increasing complexity of advancedtechnology node process flows, a large portion of the experimentalfabrication runs result in negative or null characterization results.These experimental runs are long in duration, weeks to months in the“fab” (fabrication environment), and expensive. Recent semiconductortechnology advances, including FinFET, TriGate, High-K/Metal-Gate,embedded memories and advanced patterning, have dramatically increasedthe complexity of integrated semiconductor fabrication processes. Thecost and duration of technology development using this trial-and-errorexperimental methodology has concurrently increased.

Attempts have been made to use conventional mechanical computer-aideddesign (CAD) tools and specialized technology CAD (TCAD) tools to modelsemiconductor device structures, with the goal of reducing the effortsspent on fabricating experimental wafers. General-purpose mechanical CADtools have been found inadequate because they do not automatically mimicthe material addition, removal, and modification processes that occur inan actual fab. TCAD tools, on the other hand, are physics-based modelingplatforms that simulate material composition changes that occur duringdiffusion and implant processes, but not all of the material additionand removal effects that occur during other processes that comprise anintegrated process flow. Typically, the 3D device structure is an inputto TCAD, not an output. Furthermore because of the amount of data andcomputations required for physics-based simulations of processes, TCADsimulations are practically restricted to very small regions on a chip,most often encompassing just a single transistor. In state-of-the-artsemiconductor fabrication technologies, most of the integrationchallenge concerns the interaction between processes that may be widelyseparated in the integrated process flow and the multiple differentdevices and circuits that comprise a full technology suite (transistors,resistors, capacitors, memories, etc.). Structural failures, stemmingfrom both systematic and random effects, are typically the limiter intime-to-market for a new process technology node. As such, a differentmodeling platform and approach than mechanical CAD or TCAD is requiredto cover the larger scope of concern, and to model the entire integratedprocess flow in a structurally predictive fashion.

A virtual fabrication environment for semiconductor device structuresoffers a platform for performing semiconductor process development at alower cost and higher speed than is possible with conventionaltrial-and-error physical experimentation. In contrast to conventionalCAD and TCAD environments, a virtual fabrication environment is capableof virtually modeling an integrated process flow and predicting thecomplete 3D structures of all devices and circuits that comprise a fulltechnology suite. Virtual fabrication can be described in its mostsimple form as combining a description of an integrated process sequencewith a subject design, in the form of 2D design data (masks or layout),and producing a 3D structural model that is predictive of the resultexpected from a real/physical fabrication run. A 3D structural modelincludes the geometrically accurate 3D shapes of multiple layers ofmaterials, implants, diffusions, etc. that comprise a chip or a portionof a chip. Virtual fabrication is done in a way that is primarilygeometric, however the geometry involved is instructed by the physics ofthe fabrication processes. By performing the modeling at the structurallevel of abstraction (rather than physics-based simulations),construction of the structural models can be dramatically accelerated,enabling full technology modeling, at a circuit-level area scale. Theuse of a virtual fabrication environment thus provides fast verificationof process assumptions, and visualization of the complexinterrelationship between the integrated process sequence and the 2Ddesign data.

BRIEF SUMMARY

Embodiments of the present invention provide a virtual fabricationenvironment for semiconductor device fabrication that includes ananalytics module for identifying key parameters and for performingprocess model calibration and variability analysis. More particularly,for key parameter identification, the analytics module identifiesprocess steps and/or parameters that most strongly influence an outcomeof the fabrication process. In process model calibration, the analyticsmodule adjusts the process parameters to make the 3D model beinggenerated in the virtual fabrication environment match measurements froma physical fab such as Transmission Electron Microscopy (TEM) data or aprocess target. For variability analysis, the analytics module assists auser in analyzing and understanding the variability in metrology dataobtained for a set of virtual 3D models generated in the virtualfabrication environment.

In one embodiment, a non-transitory computer-readable medium holdscomputer-executable instructions for key parameter identification in avirtual semiconductor fabrication environment. The instructions whenexecuted cause at least one computing device to receive, for asemiconductor device structure to be virtually fabricated in a computingdevice-generated virtual fabrication environment, a selection of 2Ddesign data and a process sequence that includes multiple processes. Theinstructions when executed further perform with the computing devicevirtual fabrication runs for the semiconductor device structure based ona Design of Experiment (DOE) using the 2D design data and the processsequence. The virtual fabrication runs build multiple 3D models. Theinstructions when executed also cause at least one computing device toreceive a user identification of one or more targets for thesemiconductor device structure and execute an analytics module in thevirtual fabrication environment to identify one or more outliers inmeasurement data for the one or more targets in the 3D models producedfrom the virtual fabrication runs The instructions when executed furtherreceive a user selection to add or remove one or more of the one or moreidentified outliers from the measurement data for the one or moretargets in the 3D models, the selection received via a user interfaceprovided in the virtual fabrication environment. The instructions whenexecuted additionally performs a regression analysis on the measurementdata for the one or more targets with the analytics module after theadding or removing of the selected outliers from the measurement dataand identifies one or more key parameters with the analytics modulebased on a result of the regression analysis. An identification of theidentified one or more key parameters is displayed or exported.

In another embodiment, a method for key parameter identification in avirtual semiconductor fabrication environment includes receiving, for asemiconductor device structure to be virtually fabricated in a computingdevice-generated virtual fabrication environment, a selection of 2Ddesign data and a process sequence that includes multiple processes. Themethod further performs with the computing device virtual fabricationruns for the semiconductor device structure based on a Design ofExperiment (DOE) using the 2D design data and the process sequence. Thevirtual fabrication runs build multiple 3D models. The methodadditionally receives a user identification of one or more targets forthe semiconductor device structure and executes an analytics module inthe virtual fabrication environment to identify one or more outliers inmeasurement data for the one or more targets in the 3D models producedfrom the virtual fabrication runs The method also receives a userselection to add or remove one or more of the one or more identifiedoutliers from the measurement data for the one or more targets in the 3Dmodels. The selection is received via a user interface provided in thevirtual fabrication environment. Additionally the method performs aregression analysis on the measurement data for the one or more targetswith the analytics module after the adding or removing of the selectedoutliers from the measurement data and identifies one or more keyparameters with the analytics module based on a result of the regressionanalysis. An identification of the identified one or more key parametersis displayed or exported.

In one embodiment, a virtual fabrication system includes a computingdevice equipped with a processor and configured to generate a virtualfabrication environment that includes an analytics module. The virtualfabrication environment receives, for a semiconductor device structureto be virtually fabricated, a selection of 2D design data and a processsequence that includes multiple processes and performs virtualfabrication runs for the semiconductor device structure based on aDesign of Experiment (DOE) using the 2D design data and the processsequence. The virtual fabrication runs build multiple 3D models. Thevirtual fabrication environment receives a user identification of one ormore targets for the semiconductor device structure, executes theanalytics module in the virtual fabrication environment to identify oneor more outliers in measurement data for the one or more targets in the3D models produced from the virtual fabrication runs and receives a userselection to add or remove one or more of the one or more identifiedoutliers from the measurement data for the one or more targets in the 3Dmodels, the selection received via a user interface provided in thevirtual fabrication environment. The virtual fabrication environmentperforms a regression analysis on the measurement data for the one ormore targets with the analytics module after the adding or removing ofthe selected outliers from the measurement data, identifies one or morekey parameters with the analytics module based on a result of theregression analysis, and displays or exports an identification of theidentified one or more key parameters. The virtual fabrication systemfurther includes a display surface in communication with the computingdevice. The display surface is configured to display the 3D structuralmodel in a 3D view.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate one or more embodiments of theinvention and, together with the description, help to explain theinvention. In the drawings:

FIG. 1 depicts an exemplary virtual fabrication environment suitable forpracticing an embodiment of the present invention;

FIG. 2 depicts an exemplary virtual fabrication console in the virtualfabrication environment;

FIG. 3 depicts an exemplary layout editor in the virtual fabricationenvironment;

FIG. 4 depicts an exemplary process editor in the virtual fabricationenvironment;

FIG. 5 depicts an exemplary sequence of steps in the virtual fabricationenvironment to generate virtual metrology measurement data;

FIG. 6 depicts an exemplary 3D viewer in the virtual fabricationenvironment;

FIG. 7 depicts an exemplary display of virtual metrology measurementdata in the virtual fabrication environment;

FIG. 8 depicts an exemplary sequence of steps in the virtual fabricationenvironment to calibrate a process sequence in a virtual fabricationenvironment;

FIG. 9 depicts an exemplary sequence of steps to set up and perform avirtual experiment generating virtual metrology measurement data formultiple semiconductor device structure models in the virtualfabrication environment;

FIG. 10 depicts an exemplary parameter explorer view used to provideprocess parameters for a virtual experiment in the virtual fabricationenvironment;

FIG. 11 depicts an exemplary tabular-formatted display of virtualmetrology data generated in a virtual experiment in the virtualfabrication environment;

FIG. 12 depicts an exemplary graphical display of virtual metrology datagenerated in a virtual experiment in the virtual fabricationenvironment;

FIG. 13 depicts an exemplary analytics flow in an exemplary embodiment;

FIGS. 14A-14G depict exemplary user interfaces provided by a virtualfabrication environment while identifying key parameters in an exemplaryembodiment;

FIG. 15 depicts a sequence of steps performed to identify key parametersin an exemplary embodiment;

FIG. 16 depicts a sequence of steps performed for process modelcalibration in an exemplary embodiment;

FIG. 17 depicts target selection and desired value entry optionsprovided by a process model calibration UI in an exemplary embodiment;

FIG. 18 depicts calibration options provided by a process modelcalibration UI in an exemplary embodiment;

FIG. 19 depicts parameter bound entry options provided by a processmodel calibration UI in an exemplary embodiment;

FIG. 20 depicts an exemplary display of results provided by a processmodel calibration UI in an exemplary embodiment;

FIG. 21 depicts a sequence of steps used to perform variability analysisin an exemplary embodiment;

FIG. 22 depicts an exemplary user interface displaying a variableanalysis results window in an exemplary embodiment: and

FIG. 23 depicts an exemplary user interface displaying a comparison ofvariable analysis results for separate targets in an exemplaryembodiment.

DETAILED DESCRIPTION

Embodiments of the present invention provide a virtual fabricationenvironment for semiconductor device fabrication that includes ananalytics module for identifying key parameters and for performingprocess model calibration and variability analysis. However, prior todiscussing the key parameter identification, process model calibration,optimization, variability analysis and other features provided byembodiments, an exemplary 3D design environment/virtual fabricationenvironment into which an analytics module of the present invention maybe integrated is first described.

Exemplary Virtual Fabrication Environment

FIG. 1 depicts an exemplary virtual fabrication environment 1 suitablefor practicing an embodiment of the present invention. Virtualfabrication environment 1 includes a computing device 10 accessed by auser 2. Computing device 10 is in communication with a display 120.Display 120 may be a display screen that is part of computing device 10or may be a separate display device or display surface in communicationwith computing device 10. Computing device 10 may be a PC, laptopcomputer, tablet computing device, server, or some other type ofcomputing device equipped with one or more processors 11 and able tosupport the operations of virtual fabrication application, 70, 3Dmodeling engine 75 and analytics module 79 (described further below).The processor(s) may have one or more cores. The computing device 10 mayalso include volatile and non-volatile storage such as, but not limitedto, Random Access Memory (RAM) 12, Read Only Memory (ROM) 13 and harddrive 14. Computing device 10 may also be equipped with a networkinterface 15 so as to enable communication with other computing devices.It will be appreciated that computing device 10 rather than being asolitary computing device may also be implemented as a computing systemwith multiple computing devices working in parallel or othercombination.

Computing device 10 may store and execute virtual fabricationapplication 70 including 3D modeling engine 75. 3D modeling engine 75may include one or more algorithms such as algorithm 1 (76), algorithm 2(77), and algorithm 3 (78) used in virtually fabricating semiconductordevice structures. 3D modeling engine 75 may accept input data 20 inorder to perform virtual fabrication “runs” that produce semiconductordevice structural model data 90. Virtual fabrication application 70 and3D modeling engine 75 may generate a number of user interfaces and viewsused to create and display the results of virtual fabrication runs. Forexample, virtual fabrication application 70 and 3D modeling engine 75may display layout editor 121, process editor 122 and virtualfabrication console 123 used to create virtual fabrication runs. Virtualfabrication application 70 and 3D modeling engine 75 may also display atabular and graphical metrology results view 124 and 3D view 125 forrespectively displaying results of virtual fabrication runs and 3Dstructural models generated by the 3D modeling engine 75 during virtualfabrication of semiconductor device structures. Virtual fabricationapplication 70 may also include analytics module 79 for performinganalysis of 3D models as discussed further below.

Input data 20 includes both 2D design data 30 and process sequence 40.Process sequence 40 may be composed of multiple process steps 43, 44,47, 48 and 49. As described further herein, process sequence 40 may alsoinclude one or more virtual metrology measurement process steps 45.Process sequence 40 may further include one or more subsequences whichinclude one or more of the process steps or virtual metrologymeasurement process steps. 2D design data 30 includes of one or morelayers such as layer 1 (32), layer 2 (34) and layer 3 (36), typicallyprovided in an industry-standard layout format such as GDS II (GraphicalDesign System version 2) or OASIS (Open Artwork System InterchangeStandard).

Input data 20 may also include a materials database 60 including recordsof material types such as material type 1 (62) and material type 2 (64)and specific materials for each material type. Many of the process stepsin a process sequence may refer to one or more materials in thematerials database. Each material has a name and some attributes such asa rendering color. The materials database may be stored in a separatedata structure. The materials database may have hierarchy, wherematerials may be grouped by types and sub-types. Individual steps in theprocess sequence may refer to an individual material or a parentmaterial type. The hierarchy in the materials database enables a processsequence referencing the materials database to be modified more easily.For example, in virtual fabrication of a semiconductor device structure,multiple types of oxide material may be added to the structural modelduring the course of a process sequence. After a particular oxide isadded, subsequent steps may alter that material. If there is nohierarchy in the materials database and a step that adds a new type ofoxide material is inserted in an existing process sequence, allsubsequent steps that may affect oxide materials must also be modifiedto include the new type of oxide material. With a materials databasethat supports hierarchy, steps that operate on a certain class ofmaterials such as oxides may refer only to the parent type rather than alist of materials of the same type. Then, if a step that adds a new typeof oxide material is inserted in a process sequence, there is no need tomodify subsequent steps that refer only to the oxide parent type. Thushierarchical materials make the process sequence more resilient tomodifications. A further benefit of hierarchical materials is that stockprocess steps and sequences that refer only to parent material types canbe created and re-used.

3D Modeling Engine 75 uses input data 20 to perform the sequence ofoperations/steps specified by process sequence 40. As explained furtherbelow, process sequence 40 may include one or more virtual metrologysteps 45, 49 that indicate a point in the process sequence during avirtual fabrication run at which a measurement of a structural componentshould be taken. The measurement may be taken using a locator shapepreviously added to a layer in the 2D design data 30. Alternatively, themeasurement location may be specified by alternate means such as (x, y)coordinates in the 2D design data or some other means of specifying alocation in the 2D design data 30 instead of through the use of alocator shape. The performance of the process sequence 40 during avirtual fabrication run generates virtual metrology data 80 and 3Dstructural model data 90. 3D structural model data 90 may be used togenerate a 3D view of the structural model of the semiconductor devicestructure which may be displayed in the 3D viewer 125. Virtual metrologydata 80 may be processed and presented to a user 2 in the tabular andgraphical metrology results view 124.

Because of the large number of structural dimensions that are criticalto the success of an integrated technology such as semiconductordevices, finding the relationship between the many inter-related processsteps used to fabricate a device structure and the created structure iscritical. As structural modifications produced by a step in the processsequence may be affected by previous and subsequent steps in thesequence, a particular step may affect a structural dimension in waysthat are not obvious. A virtual fabrication environment enablesautomatic extraction of structural measurements from the device beingcreated. The automatic extraction of a measurement is accomplished byspecifying a virtual metrology measurement step in the process sequenceat a point in the process when the measurement is critical. A locatorshape for this virtual metrology measurement can be added to a layer inthe design data and specified by the virtual metrology measurement step.The output data from this virtual metrology measurement can be used toprovide quantitative comparison to other modeling results or to physicalmetrology measurements. This virtual metrology measurement capability isprovided by during the processing sequence to extract a criticalphysical dimension at the correct point in the integrated process flow.

The ability to provide virtual metrology measurement data at specifiedlocations in the device structure provides a significant improvementover conventional physical fab measuring techniques. Typically, physicalin-fab measurements are done on specific characterization structuresfabricated in the scribe lines or saw kerfs, adjacent to the productdice. In most cases, these characterization structures need to bedesigned to accommodate limitations of the measurement technique, suchas optical spot size. Therefore, the characterization structures are notentirely representative of the actual structures on the product dice.Because of these differences, users of in-fab measurements usually facethe challenge of inferring the result on the product structure from ameasurement on a characterization structure. In the virtual fabricationenvironment, measurements can be added to any design layout at specifiedpoints in the process sequence thus providing greater insight into theeffect of the inter-related process steps on the virtual structuralmodel being constructed. As such, the in-fab challenge of measuring acharacterization structure and inferring the result on a productstructure is eliminated.

FIG. 2 depicts an exemplary virtual fabrication console 123 to set up avirtual fabrication run in the virtual fabrication environment. Thevirtual fabrication console 123 allows the user to specify a processsequence 202 and the layout (2D design data) 204 for the semiconductordevice structure that is being virtually fabricated. It should beappreciated however that the virtual fabrication console can also be atext-based scripting console that provides the user with a means ofentering scripting commands that specify the required input and initiatebuilding of a structural model, or building a set of structural modelscorresponding to a range of parameter values for specific steps in theprocess sequence. The latter case is considered a virtual experiment(discussed further below).

FIG. 3 depicts an exemplary layout editor in the virtual fabricationenvironment. The layout editor 121 displays the 2D design layoutspecified by the user in the virtual fabrication console 123. In thelayout editor, color may be used to depict different layers in thedesign data. The areas enclosed by shapes or polygons on each layerrepresent regions where a photoresist coating on a wafer may be eitherexposed to light or protected from light during a photolithography stepin the integrated process flow. The shapes on one or more layers may becombined (booleaned) to form a mask that is used in a photolithographystep. The layout editor 121 provides a means of inserting, deleting andmodifying a polygon on any layer, and of inserting, deleting ormodifying layers within the 2D design data. A layer can be inserted forthe sole purpose of containing shapes or polygons that indicate thelocations of virtual metrology measurements. The rectangular shapes 302,304, 306 have been added to an inserted layer (indicated by a differentcolor) and mark the locations of virtual metrology measurements. Asnoted above, other approaches to specifying the locations for thevirtual metrology measurements besides the use of locator shapes mayalso be employed in the virtual fabrication environment. The design datais used in combination with the process data and materials database tobuild a 3D structural model.

Inserted layers in the design data displayed in the layout editor 121may include inserted locator shapes. For example, a locator shape may bea rectangle, the longer sides of which indicate the direction of themeasurement in the 3D structural model. For example, in FIG. 3, a firstlocator shape 302 may mark a double patterning mandrel for virtualmetrology measurement, a second locator shape 304 may mark a gate stackfor virtual metrology measurement and a third locator shape 306 may marka transistor source or drain contact for virtual metrology measurement

FIG. 4 depicts an exemplary process editor 122 in the virtualfabrication environment. The user defines a process sequence in theprocess editor. The process sequence is an ordered list of process stepsconducted in order to virtually fabricate the user's selected structure.The process editor may be a text editor, such that each line or group oflines corresponds to a process step, or a specialized graphical userinterface such as is depicted in FIG. 4. The process sequence may behierarchical, meaning process steps may be grouped into sub-sequencesand sub-sequences of sub-sequences, etc. Generally, each step in theprocess sequence corresponds to an actual step in the fab. For instance,a sub-sequence for a reactive ion etch operation might include the stepsof spinning on photo resist, patterning the resist, and performing theetch operation. The user specifies parameters for each step or sub-stepthat are appropriate to the operation type. Some of the parameters arereferences to materials in the materials database and layers in the 2Ddesign data. For example, the parameters for a deposit operationprimitive are the material being deposited, the nominal thickness of thedeposit and the anisotropy or ratio of growth in the lateral directionversus the vertical direction. This deposit operation primitive can beused to model actual processes such as chemical vapor deposition (CVD).Similarly, the parameters for an etch operation primitive are a maskname (from the design data), a list of materials affected by theoperation, and the anisotropy.

There may be hundreds of steps in the process sequence and the processsequence may include sub-sequences. For example, as depicted in FIG. 4,a process sequence 410 may include a subsequence 412 made up of multipleprocess steps such as selected step 413. The process steps may beselected from a library of available process steps 402. For the selectedstep 413, the process editor 122 enables a user to specify all requiredparameters 420. For example, a user may be able to select a materialfrom a list of materials in the material database 404 and specify aprocess parameter 406 for the material's use in the process step 413.

One or more steps in the process sequence may be virtual metrology stepsinserted by a user. For example, the insertion of step 4.17 “Measure CD”(414), where CD denotes a critical dimension, in process sequence 412would cause a virtual metrology measurement to be taken at that point inthe virtual fabrication run using one or more locator shapes that hadbeen previously inserted on one or more layers in the 2D design data.Inserting the virtual metrology steps directly in the fabricationsequence allows virtual metrology measurements to be taken at criticalpoints of interest during the fabrication process. As the many steps inthe virtual fabrication interact in the creation of the final structure,the ability to determine geometric properties of a structure, such ascross-section dimensions and surface area, at different points in theintegrated process flow is of great interest to the process developerand structure designer.

FIG. 5 depicts an exemplary sequence of steps in the virtual fabricationenvironment to generate virtual metrology measurement data. The sequencebegins with a user selecting a semiconductor device structure to befabricated (step 502). The user may select from among multiple availablesets of design data files and then select a rectangular region withinthe design data. For example the user may choose a FinFET or a passiveresistor or a memory cell. Following the determination/selection of thestructure to be fabricated, the user enters a process sequence in theprocess editor 122 (step 504 a) and selects 2D design data that isexpected to result in the desired structure (step 504 b). Optionally,the user may create or modify design data in the layout editor 121. Inthe process editor, the user may insert one or more virtual metrologysteps in the process sequence that specify a point during the virtualfabrication that the user would like virtual metrology measurements tobe taken at specified locations in the evolving structure (step 506 a).The user may insert locator shapes in the 2D design data displayed inthe layout editor 121 that will be used by the virtual metrology step toperform its measurements (step 506 b). The significance of a locatorshape depends on the type of measurement requested. For example, thelonger axis of a rectangular shape may indicate the direction and extentof a length measurement to be taken on a cross section of the structure,or the rectangle itself may designate a region where the contact areabetween two materials is to be measured. It will be appreciated thatboth above-described steps in the process editor may be performed beforethe steps in the layout editor or vice-versa in the virtual fabricationenvironment.

After the one or more locator shapes have been added to one or morelayers in the 2D design data (step 506 b) and the virtual metrologystep(s) have been added to the process sequence (506 a) the user sets upa virtual fabrication run using the virtual fabrication console 123(step (508). During the virtual fabrication run, the process steps inthe process sequence 40 are performed in the order specified by the 3Dmodeling engine 75. When the virtual fabrication reaches the virtualmetrology step, a virtual “measurement” of the specified component inthe structure being fabricated is performed. The computations done bythe modeling engine depend on the nature of the measurement beingrequested, and are generally consistent with the analogous physicalmeasurement technique in the fab. For example, critical dimensionscanning electron microscope (CD-SEM) measurements in the fab locatesidewalls by detecting rapid changes in the orientation of the topsurface of a structure. Similarly in a virtual metrology operation, the3D modeling engine extracts the top surface of the structure in theregion specified by a locator rectangle, interrogates the surface alongits intersection with a plane defined by the intersection of the longeraxis of the rectangle and the vertical axis for changes in slope thatexceed a threshold (5 degrees, for example). Large changes in slopedefine faces of a feature, such as the bottom, top and sides of a ridgein the structure. Having established the locations of bottom, top andsides of a feature, the distance between the sides of the feature iscomputed at a vertical location (bottom, middle, or top) specified bythe metrology step. The 3D modeling engine generates one or more typesof output as it builds structural models. One type of output is thestructural model itself, and may include its state at one or more pointsin the process sequence. The 3D model may be displayed to a user in the3D viewer 125 (step 512 a). The 3D modeling engine also exports thevirtual metrology data (step 510). The virtual metrology data 80 may beexported to an automatic data analysis tool for further processing ormay be displayed to a user through a user interface such as the tabularand graphical metrology results view 124 or other view (step 512 b). Ifthe structure when viewed or analyzed is satisfactory (step 513), thevirtual fabrication run ends (step 514). If the structure created by the3D modeling engine is unsatisfactory, the user modifies the processsequence and/or the 2D design data (step 516) and a new virtualfabrication run is set up (step 508).

FIG. 6 depicts an exemplary 3D viewer 125 in the virtual fabricationenvironment. The 3D viewer 75 may include a 3D view canvas 602 fordisplaying 3D models generated by the 3D modeling engine 75. The 3Dviewer 75 may display saved states 604 in the process sequence and allowa particular state to be selected 606 and appear in the 3D view canvas.The 3D Viewer provides functionality such as zoom in/out, rotation,translation, cross section, etc. Optionally, the user may activate across section view in the 3D view canvas 602 and manipulate the locationof the cross section using a miniature top view 608.

Another type of output from the 3D modeling engine 75 is the dataproduced by virtual metrology steps that are included in the processsequence. FIG. 7 depicts an exemplary display of virtual metrologymeasurement data 80 generated by multiple virtual metrology measurementsteps in the virtual fabrication environment. The virtual metrologymeasurement result data 80 may be displayed in a tabular or graphicalform including 2D X-Y plots and multi-dimensional graphics.

The techniques employed in the exemplary virtual fabrication environmentare geometry-based. Calibration of the process step input parameterswith actual experimental results from a physical fabrication to makevirtual experiments more predictive is therefore advisable. Suchcalibration of the process steps results in improved modeling accuracyfor all structures that comprise the full technology suite. Calibrationcan be executed on individual process steps from measurements, metrologyor other physical characterization methods on characterizationstructures or product structures. Calibration may be conducted bycomparing modeling results, including virtual metrology measurementdata, to corresponding measurements or metrology conducted in thephysical fab (on corresponding characterization or product structures),and subsequently adjusting modeling parameters such that the resultingvirtually fabricated structures better match the physically fabricatedstructures. With proper calibration of modeling process parameters, thevirtual fabrication environment becomes more predictive of thestructures that result from physical fabrication throughout the entireallowed design space.

FIG. 8 depicts an exemplary sequence of steps to calibrate a processsequence in a virtual fabrication environment. The sequence includessteps taken in both a virtual fabrication environment and acorresponding physical fab environment. In the virtual fabricationenvironment, the user selects a process sequence (for a structure to bevirtually fabricated) to be calibrated and identifies related processparameters (step 802 a). In the physical fab the user identifies a setof characterization or product structures for measurement during afabrication run (step 802 b). Back in the virtual fabricationenvironment the user enters the process sequence in the process editor(step 804 a) and the 2D design data (layout) that defines thecharacterization structures is selected from available 2D design data orcreated for the purpose in the layout editor 121 (step 804 b) The samedesign data is used for virtual fabrication and actual characterization.As discussed above, the user inserts one or more virtual metrology stepsin the process sequence (step 806 a) and adds measurement locator shapesto the 2D design data (step 806 b). The user sets up a virtual fab runin the virtual fabrication console (step 808) and the 3D modeling enginebuilds the 3D model, and generates and exports virtual metrology data(step 812 a). In parallel or offset with the virtual fabrication run,the physical fabrication environment creates the characterization orproduct structures (step 810) and in-fab images and measurements aretaken on these structures (step 812 b). The user may then compare the 3Dviews of the generated virtual model in the 3D viewer 75 to the in-fabimages of the physical device structure (step 814 a). Further, the setof characterization structure measurements may be compared to thevirtual metrology measurements taken as a result of the virtualmetrology step being inserted into the process sequence (step 814 b). Inmost cases, this comparison will be made by the user, but alternativelythe comparison may be made by an automated data analysis tool based onpre-defined or interactively solicited criteria. If there issatisfactory agreement between the views and images and the virtual andactual measurements (step 815), the process sequence is consideredcalibrated (step 816). However, if there is not satisfactory agreement(step 815), the user modifies the values of the process parameters inthe process editor (step 818) and a new virtual fabrication run is setup in the virtual fabrication console (step 808). The sequence theniterates until a satisfactory agreement is reached and calibration isachieved.

It should be appreciated that there may be a number of differentparameters that may be calibrated within the sequence. Although theabove description notes the use of the insertion of virtual metrologysteps in the process sequence and the related use of the 2D locatorshape or shapes to conduct the virtual metrology measurements, othertechniques could be employed in the in a virtual fabricationenvironment. For example, the virtual measurements could be conducted ona virtual device structure after fabrication is completed and thencompared to the physical measurements taken of the characterizationstructures during/after the physical fabrication run.

While building a single structural model can be valuable, there isincreased value in virtual fabrication that builds a large number ofmodels. A virtual fabrication environment may enable a user to createand run a virtual experiment. In a virtual experiment, a range of valuesof process parameters can be explored. A virtual experiment may be setup by specifying a set of parameter values to be applied to individualprocesses (rather than a single value per parameter) in the full processsequence. A single process sequence or multiple process sequences can bespecified this way. The 3D modeling engine 75, executing in virtualexperiment mode, then builds multiple models spanning the processparameter set, all the while utilizing the virtual metrology measurementoperations described above to extract metrology measurement data foreach variation. This capability may be used to mimic two fundamentaltypes of experiments that are typically performed in the physical fabenvironment. Firstly, fabrication processes vary naturally in astochastic (non-deterministic) fashion. As explained herein, afundamentally deterministic approach used for each virtual fabricationrun nevertheless can predict non-deterministic results by conductingmultiple runs. A virtual experiment mode allows the virtual fabricationenvironment to model through the entire statistical range of variationfor each process parameter, and the combination of variations inmany/all process parameters. Secondly, experiments run in the physicalfab may specify a set of parameters to be intentionally varied whenfabricating different wafers. The virtual experiment mode enables theVirtual Fabrication Environment to mimic this type of experiment aswell, by performing multiple virtual fabrication runs on the specificvariations of a parameter set.

Each process in the fabrication sequence has its own inherent variation.To understand the effect of all the aggregated process variations in acomplex flow is quite difficult, especially when factoring in thestatistical probabilities of the combinations of variations. Once avirtual experiment is created, the process sequence is essentiallydescribed by the combination of numerical process parameters included inthe process description. Each of these parameters can be characterizedby its total variation (in terms of standard deviation or sigma values),and therefore by multiple points on a Gaussian distribution or otherappropriate probability distribution. If the virtual experiment isdesigned and executed to examine all of the combinations of the processvariations (multiple points on each Gaussian, for example the ±3 sigma,±2 sigma, ±1 sigma, and nominal values of each parameter), then theresulting graphical and numerical outputs from virtual metrology stepsin the sequence cover the total variation space of the technology. Eventhough each case in this experimental study is modeled deterministicallyby the virtual fabrication system, the aggregation of the virtualmetrology results contains a statistical distribution. Simplestatistical analysis, such as Root Sum Squares (RSS) calculation of thestatistically uncorrelated parameters, can be used to attribute a totalvariation metric to each case of the experiment. Then, all of thevirtual metrology output, both numerical and graphical, can be analyzedrelative to the total variation metric.

In typical trial-and-error experimental practice in a physical fab, astructural measurement resulting from the nominal process is targeted,and process variations are accounted for by specifying an overly large(conservative) margin for the total variation in the structuralmeasurement (total structural margin) which must be anticipated insubsequent processes. In contrast, the virtual experiment in the virtualfabrication environment can provide quantitative predictions of thetotal variation envelope for a structural measurement at any point inthe integrated process flow. The total variation envelope, rather thanthe nominal value, of the structural measurement may then become thedevelopment target. This approach can ensure acceptable total structuralmargin throughout the integrated process flow, without sacrificingcritical structural design goals. This approach, of targeting totalvariation may result in a nominal intermediate or final structure thatis less optimal (or less aesthetically pleasing) than the nominalstructure that would have been produced by targeting the nominalprocess. However, this sub-optimal nominal process is not critical,since the envelope of total process variation has been accounted for andis more important in determining the robustness and yield of theintegrated process flow. This approach is a paradigm shift insemiconductor technology development, from an emphasis on the nominalprocess to an emphasis on the envelope of total process variation.

FIG. 9 depicts an exemplary sequence of steps in the virtual fabricationenvironment to set up and perform a virtual experiment generatingvirtual metrology measurement data for multiple semiconductor devicestructural models. The sequence begins with a user selecting a processsequence (which may have been previously calibrated to make the resultsmore structurally predictive (step 902 a) and identifying/creating 2Ddesign data (step 902 b). The user may select process parametervariations to analyze (step 904 a) and/or design parameter variations toanalyze (step 904 b). The user inserts one or more virtual metrologysteps in the process sequence as set forth above (step 906 a) and addsmeasurement locator shapes to the 2D design data (step 906 b). The usermay set up the virtual experiment with the aid of a specialized userinterface, an automatic parameter explorer 126 (step 908). An exemplaryautomatic parameter explorer is depicted in FIG. 10 and may display, andallow the user to vary, the process parameters to be varied 1002, 1004,1006 and the list of 3D models to be built with their correspondingdifferent parameter values 1008. The parameter ranges for a virtualexperiment can be specified in a tabular format. The 3D modeling engine75 builds the 3D models and exports the virtual metrology measurementdata for review (step 910). The virtual experiment mode provides outputdata handling from all Virtual Measurement/Metrology operations. Theoutput data from the virtual metrology measurements may be parsed andassembled into a useful form (step 912).

With this parsing and assembling, subsequent quantitative andstatistical analysis can be conducted. A separate output data collectormodule 110 may be used to collect 3D model data and virtual metrologymeasurement results from the sequence of virtual fabrication runs thatcomprise the virtual experiment and present them in graphical andtabular formats. FIG. 11 depicts an exemplary tabular-formatted displayof virtual metrology data generated by a virtual experiment in thevirtual fabrication environment. In the tabular formatted display, thevirtual metrology data collected during the virtual experiment 1102 andthe list of virtual fabrication runs 1104 may be displayed.

FIG. 12 depicts an exemplary 2D X-Y graphical plot display of virtualmetrology data generated by a virtual experiment in the virtualfabrication environment. In the example depicted in FIG. 10, the totalvariation in shallow trench isolation (STI) step height due to varying 3parameters in preceding steps of the process sequence is shown. Eachdiamond 1202 represents a virtual fabrication run. The variationenvelope 1204 is also displayed as is the depicted conclusion 1206 thatthe downstream process modules must support approximately 10.5 nm oftotal variation in STI step height to achieve robustness through 6 sigmaof incoming variation. The virtual experiment results can also bedisplayed in multi-dimensional graphic formats.

Once the results of the virtual experiment have been assembled, the usercan review 3D models that have been generated in the 3D viewer (step 914a) and review the virtual metrology measurement data and metricspresented for each virtual fabrication run (step 914 b). Depending onthe purpose of the virtual experiment, the user can analyze the outputfrom the 3D modeling engine for purposes of developing a processsequence that achieves a desired nominal structural model, for furthercalibrating process step input parameters, or for optimizing a processsequence to achieve a desired process window.

The 3D modeling engine's 75 task of constructing multiple structuralmodels for a range of parameter values (comprising a virtual experiment)is very compute intensive and therefore could require a very long time(many days or weeks) if performed on a single computing device. Toprovide the intended value of virtual fabrication, model building for avirtual experiment must occur many times faster than a physicalexperiment. Achieving this goal with present day computers requiresexploiting any and all opportunities for parallelism. The 3D modelingengine 75 uses multiple cores and/or processors to perform individualmodeling steps. In addition, the structural models for differentparameter values in a set are completely independent and can thereforebe built in parallel using multiple cores, multiple processors, ormultiple systems.

The 3D modeling engine 75 in the virtual fabrication environment mayrepresent the underlying structural model in the form of voxels. Voxelsare essentially 3D pixels. Each voxel is a cube of the same size, andmay contain one or more materials, or no materials. Those skilled in theart will recognize that the 3D modeling engine 75 may also represent thestructural model in other formats. For instance, the 3D modeling enginecould use a conventional NURBS-based solid modeling kernel such as isused in 3D mechanical CAD tools, although modeling operations based on adigital voxel representation are far more robust than the correspondingoperations in a conventional analog solid modeling kernel. Such solidmodeling kernels generally rely on a large number of heuristic rules todeal with various geometric situations, and modeling operations may failwhen the heuristic rules do not properly anticipate a situation. Aspectsof semiconductor structural modeling that cause problems for NURBS-basedsolid modeling kernels include the very thin layers produced bydeposition processes and propagation of etch fronts that results inmerging faces and/or fragmentation of geometry.

The virtual fabrication environment may enable the performance of amulti-etch process that is included in the process sequence which allowsthe 3D modeling engine 75 to model a wide-range of process andmaterial-specific etch behavior. Patterning operations in process flowsfor highly scaled semiconductor devices are frequently performed usingplasma etches. Plasma etches are known by many different names: dryetch, reactive ion etch (RIE), inductively coupled plasma (ICP) etch,etc. A wide variety of operating conditions and chemistry allows processengineers to fine-tune plasma etch behavior to selectively achievediverse etch physics in multiple different classes of materials. Thisbehavioral flexibility is key to achieving a desired 3D structure whenpatterning through several layers of material. Several different typesof physics are typically involved, including but not limited to:chemical etching, sputtering, deposition or re-deposition of polymericmaterial, electrostatic charging, electrostatic focusing, and shadowing.This diverse spectrum of physics produces a commensurate range of etchbehavior and hence structural shapes.

Directly simulating the physics involved in plasma etches withsufficient accuracy is extremely difficult and slow. The multi-etchprocess step avoids the difficulties of physics-based simulations bysimulating plasma etches using a reduced set of behavioral parametersthat are specific to the type of etch and the material being etched.This allows the capture of a wide range of physical etch behaviorwithout the need to directly simulate the physics of the etch process.For example, three main types of etch behavior may be simulated:isotropic, taper, and sputtering. A fourth type of etch behavior,shadowing, can optionally also be simulated.

Basic (isotropic) behavior is caused (physically) by chemical etchingand results in material being removed at a similar rate in alldirections from the point on the etchable surface, regardless of thelocal orientation of the etchable surface. Basic behavior may be modeledwith a single input parameter, “lateral ratio”, that controls the ratiobetween the lateral and vertical etch rates. For example, a lateralratio value of one (1.0) indicates that the etch rate is uniform in alldirections. A lateral ratio value less than one indicates that the etchrate in the lateral direction (on vertical surfaces) is slower than theetch rate in the vertical direction (on horizontal surfaces).

Taper behavior is caused (physically) by a combination of directionaletch behavior and polymer deposition. The polymer deposition occurs as aside effect of a directional etch process. During a directional etchprocess that etches horizontal surfaces much faster than verticalsurfaces, polymer may accumulate on near-vertical surfaces. Thiscompetition between etching and deposition results in tapered sidewallprofiles. Taper behavior may be modeled with a single input parameter,the taper angle. A taper angle describes the critical angle at whichdeposition and etch rates are balanced. An optional second parameter,the lateral ratio, has the same meaning as defined above for basicbehavior.

Sputter behavior refers to direct physical removal of material throughbombardment by energetic ions and results in preferential removal ofprotruding edges (convex edges) and in some cases corners. Sputteringmay be modeled with two parameters: the angle of maximum sputter yield,and the rate of sputter relative to the rate of vertical etching.

Shadowing refers to a reduction in directional ion flux caused by alocal elevation change, effectively reducing etch rates for somestructures. This effect can be significant in some cases, resulting indiffering etch rates across a cell. Shadowing may be modeled using asingle parameter to describe angle of incidence of the energetic ionsrelative to a vertical axis.

To model a multi-material, multi-physics etch, the input parametersdescribed above must be formed into a suitable numerical modelingalgorithm in the virtual fabrication environment. The numerical modelingalgorithm includes single material and multi-material speed functionsand a surface evolution technique. A single-material speed functiondefines the etch speed as a function of local surface orientation (i.e.,surface normal direction) and is determined empirically in order toproduce the desired etch behavior. Note also that a single-materialspeed function may combine multiple types of etch behavior; for example,both taper and sputter etching include the parameters associated withbasic (isotropic) etching. A multi-material speed function is acombination of single-material speed functions, and calculates the localetch speed as a function of both local surface orientation and localmaterial type. The Etch Ratio parameter defines the relative etch ratesof etchable materials and is a multiplication factor on thesingle-material speed.

With the speed function defined, a suitable surface evolution techniquemay be used to locate and evolve the position of the etchable surface inthree dimensions. The etchable surface is advected or moved in its localnormal direction according to the local scalar speed determined byevaluating the speed function. The scalar speed must be calculated atpoints of interest on the etchable surface and must be periodicallyre-calculated as the geometry of the etchable surface evolves.

A number of different types of surface evolution techniques may beutilized by the numerical algorithm for simulating the multi-etchprocess in the virtual fabrication environment. The moving surface maybe represented using any suitable numerical spatial discretization.Explicit front tracking methods may be used: examples include stringmethods, point-and-line methods (2D) and polygon surfaces (3D). Analternate implicit surface representation, such as distance fields,volume of fluid or voxels, may also be used. Any suitable time-dependentnumerical technique may be used to advance the moving surface in time.

A selective epitaxy process may be included in a process sequence usedto virtually fabricate a semiconductor device structure. The selectiveepitaxy process virtually models epitaxial growth of a crystallinematerial layer on top of a crystalline substrate surface of asemiconductor device structure. Selective epitaxy is widely used incontemporary semiconductor process flows, often for the purpose ofimparting mechanical stress on the transistor channel to improveperformance. A key characteristic of epitaxial growth is its dependenceon crystal directions. Semiconductor devices are normally fabricated onsingle crystal silicon wafers; i.e., silicon material with atomsarranged in a repetitive crystal lattice structure that is continuousover the majority of the wafer. Silicon crystal structure is anisotropic(i.e., not symmetric in all directions), and silicon surfaces are morestable in several particular crystal directions. These directions aredefined by the major crystal plane families, identified as <100>, <110>and <111> using their Miller indices, and have the strongest impact ongrowth characteristics. By varying the pressure, temperature andchemical precursors in the epitaxy process, engineers can control therelative growth rates of the three major planes. Growth rates on minorplanes, for example <211>, <311>, <411>, also vary but often are notinfluential in determining the final shape of an epitaxially grownstructure.

The virtual fabrication environment may use a surface evolutionalgorithm to model epitaxial growth. The surface upon which epitaxialgrowth is occurring (the growing surface) is advected or moved accordingto a scalar advection speed. The growth rate is calculated at selectedpoints based on the local surface normal direction and fixed inputparameters, is local in both distance and time, and moves the surface inits normal direction. The growing surface may be represented using anysuitable numerical spatial discretization. Explicit front trackingmethods may be used: examples include string methods, point-and-linemethods (2D) and polygon surfaces (3D). An alternate implicit surfacerepresentation, such as distance functions, volume of fluid or voxels,may also be used. Any suitable time-dependent numerical technique may beused to advance the growing surface in time.

The selective epitaxy process in the virtual fabrication environmentutilizes the growth rates of the three major plane families, <100>,<110> and <111> as fixed input parameters. These input parameters definethe growth rate for surfaces that are aligned with any one of theirassociated planes. Further input parameters may include growth rates onneighboring non-crystalline materials. The relationship between the 3Dmodeling coordinate system and the crystal lattice of the wafer may alsobe considered when calculating the epitaxial growth rate. The 3Dmodeling coordinate system normally uses the same X and Y axes as the 2Ddesign data and the Z axis is normally perpendicular to the surface ofthe wafer. Alternate coordinate systems may also be employed. On a realwafer, the orientation of the crystal lattice is indicated by a “flat”or “notch” on the edge of the otherwise circular wafer. The notch may beused as a reference to orient the 2D design data in the desireddirection relative to the crystal lattice. Input parameters specifyingthe notch (or flat) type and direction may define the orientation of thecrystal lattice and associated crystal planes of the wafer relative tothe 2D design data. It should be noted that this relationship can bedescribed as a coordinate transformation between the 3D model coordinatesystem and the coordinate system of the crystal lattice.

Using the growth rates for the major plane families and knowing theorientation of the crystal lattice, the epitaxial growth rate may becalculated everywhere on the growing surface. Areas of the growingsurface with a normal direction that is aligned with a major planedirection are assigned the speed of that major plane. For areas of thegrowing surface that are not aligned with a major plane direction, anappropriate speed must be found by interpolating between neighboringmajor plane directions. Further, the behavior of the epitaxial growth atthe boundaries of the crystalline material can also be important.Epitaxial growth is often performed after several prior processing stepsin which non-crystalline materials have been deposited and patterned.These non-crystalline materials may be adjacent to crystalline materialand hence in close proximity to epitaxial growth. Examples ofnon-crystalline neighboring materials are silicon dioxide, siliconnitride, or any other materials common in semiconductor processing. Insome cases, epitaxial growth slowly creeps along adjacentnon-crystalline material (overgrowth) but in other cases it does not.Overgrowth behavior may be modeled with fixed input parameters definingthe set of neighboring materials on which overgrowth occurs (overgrowthmaterials), as well as the speed at which the growing surface creepsalong the overgrowth materials. The overgrowth speed modifies theepitaxial growth rate at the surface of the overgrowth materials suchthat the growing surface moves along the overgrowth material at thespecified speed. In addition, the speed at which the growing surfacemoves along the overgrowth material may depend on the angle between theovergrowth material surface and the growing surface. The overgrowthspeed may be ignored if the angle between the two surfaces is greaterthan a threshold angle.

Design Rule Checks (DRCs) or Optical Rule Checks (ORCs) may be performedin the virtual fabrication environment. DRCs and ORCs have typicallybeen performed by specialized software on 2D design data as part of theprocess of preparing 2D design data for conversion into photolithographymasks. Such checks are performed for purposes of identifying errors inthe layout that would result in non-functional or poorly functioningchips. The checks are also performed after adding compensations foroptical effects such as optical proximity correction (OPC). Typicaldesign rules (as published in design manuals and coded in DRC decks) aresimple 2D criteria intended to prevent problems that are fundamentally3D in nature. However, with the growing complexity of semiconductorprocess technology, design manuals have blossomed into thousand-pagedocuments with thousands of 2D design rules to codify and explain. Inmany cases, a single 3D failure mechanism/concern can drive hundreds of2D design rules. The development of those 2D design rules requiressignificant assumptions about the 3D nature of the integrated processflow and resulting structures.

2D DRCs are developed from relatively simple calculations that mayresult in overly conservative designs. For example, consider the 2Ddesign rules required to assure a minimum contact area between a line ona metal interconnect layer and an underlying via. A via is a vertical,electrically conductive connector between two interconnect layers, alsocalled metal layers, or a vertical connector between an interconnectlayer and a device such as a transistor, resistor or capacitor.

Many additional 2D DRCs are required to satisfy a criterion that is verysimple to state in 3D: that the contact area between metal lines andvias must exceed a specified threshold value. The 2D DRC situationbecomes even more complex when one considers that multiple manufacturingvariations can affect the contact area, including over or under-exposureduring lithography steps, mis-registration of the masks, planarization(via chemical mechanical polishing (CMP)) of the via layer, and thesidewall tapers produced by plasma etching. It is infeasible to includeall of these statistical variations in the simple formulae that drive 2DDRCs, so the DRCs are stricter than necessary to guard againstmanufacturing variations. These overly strict 2D DRCs may result insub-optimal designs with wasted area on the die.

In contrast to a 2D DRC environment, a virtual fabrication environmentmay perform checks, such as minimum line width, minimum space betweenfeatures, and minimum area of contacts, directly in 3D without makingassumptions about the translation from 2D to 3D. Checks performeddirectly in 3D are referred to herein as “3D DRCs”. One benefit of 3DDRC is that the required number of checks is significantly smaller thanthe number required in 2D environments. As a result, the checks are morerobust and easier to develop than 2D checks. Furthermore, with a muchsmaller set of 3D rules, the virtual fabrication environment can performthe checks for a range of statistical variations in process parameters.

It should be appreciated that 3D-DRCs are distinct from virtualmeasurement/metrology operations that may also be performed in thevirtual fabrication environment. The virtual measurement metrologyoperations mimic actual measurement and metrology operations in the fab,whereby a measurement location is specified and a metric such as adistance value or area is output. For 3D DRCs, on the other hand, ageometric criterion is specified and the location and value of thecriterion are desired. That is, the location is an output of the 3D DRCoperation rather than an input. For example, a virtual metrologyoperation may specify an oxide film thickness measurement at a specificlocation indicated by a locator in the 2D design data, whereas a 3D DRCfor minimum layer thickness may request the location(s) anywhere in the3D model where the oxide film thickness is less than a specifiedthreshold value. The 3D structural model may then be searched forlocations where the specified minimum dimensional criteria aresatisfied. Similarly, a 3D DRC may also cause the structural model to besearched to see if a maximum dimensional criteria is satisfied. 3D DRCsof this type thus provide benefits unavailable with virtualmeasurement/metrology operations for identifying unexpected causes offailures.

Examples of 3D-DRCs include:

Electrical Net Isolation: finds the shortest distance between selectedconductors. A conductor is a lump that may be comprised of one or moreconducting materials (a “lump” is a discrete volumetric region(technically, a 3-manifold) within a 3D structural model. A lump may becomposed of a single material or multiple materials);

Minimum Separation: finds the shortest distance between any pair in agroup of selected lumps;

Minimum Line Width, finds the shortest distance through any lump in agroup of selected lumps;

Minimum Layer Thickness, finds the shortest distance through any lump inthe collection of lumps that comprise a layer of material;

Minimum Contact Area: finds the smallest contact area between all pairsof selected lumps.

Lumps may be selected on the basis of constituent material(s),electrical conductivity or other properties. Each of the 3D DRC checkscan be extended by specifying a threshold value. For example, specifyinga threshold value for a Minimum Line Width check produces a list oflocations where the minimum line width is less than the threshold value.Those skilled in the art will recognize that other checks of this naturemay be defined.

Analytics Module

In one embodiment, the virtual fabrication environment includes ananalytics module. The analytics module is designed to mimic theworkflows in use cases encountered by semiconductor process integrators.Exemplary use cases encountered by semiconductor process integrators andaddressed by the analytics module may include but are not limited to,key parameter identification, process model calibration and variabilityanalysis. In key parameter identification, the analysis module may findprocess steps/parameters that most strongly influence an outcome(calibration, defect mode, etc.). In process model calibration, theprocess parameters may be adjusted to make the 3D model matchmeasurements from a physical fab, such as, but not limited to,Transmission Electron Microscopy (TEM) data or a process target. Invariability analysis, the analytics module may assist the user inanalyzing and understanding the variability in metrology data obtainedfor a set of virtual 3D models such as, but not limited to, byestimating variability in structural or electrical parameters forspecification limit setting.

The analytics module described herein may generate process variation viaexperimental design or Monte Carlo simulation applied to parameters andsettings in the virtual semiconductor fabrication environment and thenperform automated statistical analysis, optimization, and visualizationfor users. The data being analyzed can include the settings of the inputprocess parameters as well as, but not limited to, the metrology,structure search, DTC checks, and electrical analysis, that areevaluated on the 3D virtual semiconductor structures produced in thevirtual fabrication environment. Embodiments utilize statistical methodschosen and customized to solve problems and address issues peculiar tovirtual semiconductor fabrication and correct for errors that may occurwhen exporting result data to conventional third party statisticaltools.

Embodiments also provide a more efficient technique for experimentaldesign as the particular manner in which the virtual semiconductorfabrication environment of the present invention constructs 3D modelsresults in not having certain common problems that other experimentaldesign methods must address. For example, if the deck and the parametersettings are not changed, the same 3D model will be generated each andevery time in the virtual semiconductor fabrication environment. Thusthere is no random component to the 3D model output and the three commontasks in experimental design of randomization, replication and blockingare not needed to be performed.

In one embodiment, the analytics module is integrated into the virtualfabrication environment resulting in improved and new functionality notavailable via third party statistical solutions. In one embodiment, theUI and algorithms may be organized by use cases and follow a left-side,step-wise flow UI for each use case. This design may strongly guide theuser (who may lack statistical training) to perform correct analysissteps so that they avoid mistakes in the analysis. The analytics modulemay also include a statistical analysis engine that employs a set ofanalysis algorithms to correctly analyze each specific use case. Theanalytics module may solve problems not correctly addressed by thirdparty statistical software such as multicollinearity and outliers(discussed below), and, as previously noted, avoids using methods thatare not required, e.g., randomization during experimental design.Results of the analysis may be provided to a user or to third partysoftware in a number of formats.

FIG. 13 depicts an exemplary analytics flow in an exemplary embodiment.Inputs to the analytics module may include, but are not limited to,selection of the type of analysis, which may be organized by use case(e.g. identifying key parameters, optimization, calibration, variabilityanalysis). Additional exemplary inputs include process parameters ofinterest (e.g. specified as nominal values and/or ranges) and targets ofinterest (e.g.: metrology values, structure searches, DTC checks,electrical analysis values). In one embodiment, an input value may be areference to a 3D model file. The analytics module may perform run listgeneration to set up the experimental Design of Experiments (DOE) (e.g.a screening D.O.E., a full factorial D.O.E., a Monte Carlo simulation)followed by run list execution and may utilize cluster computing toincrease efficiency during execution. Outputs from execution may includeoutlier detection and statistical analysis results such as determiningparameter significance/ranking. Outputs may also include exploratorygraphs (e.g. bivariate plots, response surface) and indirectoptimization. In one embodiment results may also be exported to thirdparty tools for further analysis.

Key Parameter Identification

One exemplary use case for an embodiment employing an analytics moduleas described herein is key parameter identification. In key parameteridentification the analytics module receives a user selection of a deckcontaining a 2D layout and process steps. The purpose of the keyparameter identification use case is to determine which parameters arerelated to and affect a target. Then, those parameters are ranked toshow their relative importance. In one embodiment, the use case hasseven steps:

1) Pick experimental design;

2) Select parameters to vary and input user-selected levels into design;

3) Generate design and run (export if necessary);

4) Select metrology targets;

5) Set regression options;

6) Select identified outliers for addition or removal from DOE resultdata; and

7) Run regression and view results. Identify important/key parameters.

In this embodiment, the first step is a selection of a Design ofExperiments (DOE) step, also call experimental design. D.O.E. is amethodology for calculating the number of experiments at specificcombinations of parameters settings such that more information is gainedfor less experimental effort. The analytics module provides three waysto create an experimental design to sample the parameter space: fullfactorial design, Definitive Screening Design (DSD) and Monte Carlosimulation. FIG. 14A depicts an exemplary UI 1400 provided in thevirtual fabrication environment for making the selection of the type ofexperimental design 1402.

Full factorial design is the most classic experimental design. Allpossible combinations are created. Full factorial designs are best usedwhen the number of parameters are smaller, approximately from 2 to 7.For each parameter setting chosen, the user inputs the number of levelsand the values for those levels via the UI. In one embodiment up to 10levels can be input for each parameter setting.

Definitive Screening Design (DSD) is a screening design used when thenumber of parameters is larger or the cost (time) of runs is high. Itproduces far fewer runs than full factorial designs for the same numberof parameters. Embodiments may implement the DSD-augmented method forcontinuous variables only. In one embodiment, for a DSD, there are onlythree levels specified for each parameter.

Monte Carlo simulation is a D.O.E. option that allows for randomgeneration of parameter settings using normal or uniform distributions.In an embodiment, the UI allows the user to input means and standarddeviations for normally distributed parameters, or minima and maxima foruniformly distributed parameters, and random values are generatedaccordingly. In an embodiment the user may also enter the number of runsdesired.

FIG. 14B depicts an exemplary UI 1410 in an embodiment by which a usercan specify the levels for each parameter being varied in the design.FIG. 14B shows a screenshot for selecting parameters for a fullfactorial DOE. The left pane contains the list 1412 of parameters in thedeck. Each can be selected and added to the right pane. There, the userinputs the desired number of levels 1414 and values 1416 for each level.For example if three parameters have been selected and they have 3, 2,and 4 levels respectively they would produce 3*2*4=24 runs.

In an embodiment, the D.O.E. that has been created in the previous stepsis run by the virtual semiconductor fabrication environment in batchmode, producing a 3D model for each run in the DOE. The D.O.E. may beexported to a csv or other type of file as well.

In the fourth step of the key parameter identification workflow, themetrology targets may be selected by the user to acquire measurements onthe 3D models produced by the DOE. An exemplary UI 1420 for making theselection of metrology targets 1422 is depicted in FIG. 14C.

To perform key parameter identification, a regression model is built inthe fifth step of the workflow. In FIG. 14D, in an exemplary embodiment,the UI 1430 enables the user to select 1432 whether to build aregression model with main effects (original parameters) only, or tobuild a full quadratic model. In another embodiment, the type ofregression model is automatically selected. In one embodiment, defaultoptions may be provided for either type of regression model and may bechanged by a user. In another embodiment there may be additional optionsprovided for more knowledgeable users. These additional options 1434 mayinclude a cutoff for a collinearity test and two entry/exit p-valuecutoffs for stepwise linear regression. The collinearity test enablescorrect handling of multicollinear variables and correct identificationand exclusion of outliers from the statistical analysis being performedwithin the virtual semiconductor fabrication environment.Multicollinearity occurs when two or more predictor/independentvariables in a multiple regression model are highly correlated such thatone can be predicted from the others with a high degree of accuracy. Thefitting of a quadratic model often produces multicollinear variables andembodiments address this issue as described further below.

Within the set of 3D models created from the experimental design, one ormore 3D models may have targets (metrology, CD, etc.) containing datavalues that are unusual in some respect (outliers) that would adverselyaffect or prevent a (correct) statistical analysis. The analytics moduleidentifies outliers for the user. In FIG. 14E, in an exemplaryembodiment the UI 1440 enables the user to select from among identifiedoutliers 1442 to determine which should be omitted from the target datawhen performing statistical analysis. There are four types of outliersthat are tested for in a target in this step. Empty cells—Empty datacell returned for a target if the run failed (no 3D model could bebuilt). This type of run is marked automatically as an outlier to beremoved during statistical analysis and cannot be put back in by theuser. NOVAL—If a run completed, but the target measurement could not becalculated, a text value of “NOVAL” is returned. This type of run ismarked automatically as an outlier to be removed during statisticalanalysis and cannot be put back in by the user. Constant Values—Multiplevalues for a target may be identical. If many results for a target areidentical, this will prevent or distort statistical modeling. The targetdata is tested to check if a certain amount of data, for example 50% ormore of the data, is identical/constant by comparing it to the median.Those runs are removed. If all the target data is identical, an error isreported. Statistical Outliers—These are data points that aresufficiently far from the center of the data that they may need to beexcluded from the analysis. The Median Absolute Deviation (MAD) methodmay be used to statistically test if each data point is an outlier.Given that MAD=median(|x−median(x)|), a robust equivalent to thestandard deviation may be calculated as SM=1.4826*MAD. Data valuesexceeding MAD±K*SM (where K=3 by default and is equivalent to 3 standarddeviations) may be considered outliers and marked as such for userinspection. In one embodiment users may place any of these outliers backinto the analysis. It should be appreciated that there can be outliersin measured data that are not a concern when using the types of designsdiscussed here, i.e. DSD, full factorial or Monte Carlo simulation,since by definition, those data points are in-range, unless the user hasmade a typographical or other error in setting the levels/ranges.

Following removal of the outliers, a number of types of statisticalanalysis may be performed on the data for the targets. For example, inone embodiment, the analytics module may make input parameters for aregression model (squares/cross-terms if selected). This permits fittingbasic curved relationships between the x parameters and the target y. Aset of variables X can be fit to a linear regression model and theequation can be represented in linear algebra notation as: X*b=y, whereX is a matrix with n rows (the runs) and k columns (the variables). Inan embodiment, the analytics module can also perform a multicollinearitycheck for all possible pairs of input variables, calculate thecorrelation coefficient r, and remove one parameter of every pairwith >0.9 (this cutoff can be adjusted by the user). This fixes themulticollinearity problem in most cases.

In an embodiment, the analytics module can also perform an undeterminedmatrix check to check if X is underdetermined (k>n). If there are morevariables than data points (runs), there is not enough data to find aunique regression solution using standard equations (algorithms fail toreturn an answer). There are two solutions: 1) delete variables (useonly main effects instead of a full 2^(nd) order model), or 2) use amethod like principal component regression. In one embodiment the firsttype of solution is applied by the analytics module to delete variables.If k>p, then the squares and cross-terms are removed and checked again.If X is still underdetermined, the regression cannot be performed and anerror is returned to the user.

The analytics module may further run a number check on the data. Afteroutlier deletion, depending on the design chosen by the user and itssize, there may not be enough runs left to bother with a regression. Inone embodiment the check is to determine if the number of runs n is <10in which case there is not enough data and an error is returned to theuser.

In an embodiment, the analytics module may perform stepwise linearregression. The forward approach may be used: the initial model includesonly an intercept (the β₀ weight) and all variables are tested forstatistical significance to see which one, if any should enter themodel. Once a variable is chosen, say variable x3, then all theremaining variables are tested for inclusion into the new model. Thisprocess continues until no variables meet the inclusion criteria (ap-value <0.05, user adjustable). Variables in the model are also testedfor removal (a p-value >0.10, user adjustable).

In an embodiment the analytics module may perform a relative importancecalculation to identify key parameters. If a model is generated with twoor more statistically significant parameters, a new linear regression iscalculated using only those variables, but after they have beenautoscaled. To autoscale a variable, the variable's mean is subtractedfrom all data points and then the resulting values are divided by thevariable's original standard deviation. This makes all the variableshave a mean of 0 and a standard deviation of 1. The reason for doingthis is variable scale. One variable may be in a range 0 to 1, whileanother variable may be in a range 50 to 80. Importance (size ofweights, the β values) in regression is affected by variable scale. Ifone wants to know which variables are more important by examining the βvalues, the variables in the regression model have to be converted tohave the same variance, which autoscaling accomplishes.

The results may be presented via a user interface 1450 to the user in anumber of different formats, such as, but not limited to, a plot withannotation 1452 and in a table 1454 as depicted in FIG. 14F. The plot isa plot of predicted target vs. actual target. In one embodiment it maybe annotated with the following: r2 (regression squared correlationcoefficient, ranging from 0 to 1, indicates fraction of target variationexplained by the model), Root-Mean-Squared-Error (RMSE, a measure ofpredictive accuracy), and n (the actual number of data points/runs usedin the regression model). In one embodiment the output table 1454 ofregression results may have five columns as depicted in larger form inFIG. 14G. Column 1: Parameter Names. These are the names of the originalvariables, and if included, the square and cross-terms. Column 2:p-value for significant variables Column 3: Regression weights (β).Column 4: Relative Weight. Regression weights (β) for a regressioncalculated with autoscaled variables. These can be used to rank thesignificant parameters. For example, a parameter Etch4 lateral ratio maybe determined to be more important than Etch1 etchratio when therelative importance is calculated. Column 5. Status. In one embodimentthere are four possible results: non-significant, significant, removedhighly collinear and removed underdetermined. In an embodiment,significant parameters have non-zero weights and scaled importance thatindicate how important a given process parameter is for the chosenmetrology.

This approach to key parameter identification is further summarized inFIG. 15 which depicts a sequence of steps performed to identify keyparameters in an exemplary embodiment. The sequence begins with thereceipt of a user identification of a deck (layout data and processsteps) by the virtual fabrication environment (step 1500). Multiplevirtual fabrication runs are then performed for a D.O.E. for thesemiconductor device of interest (step 1502). In one embodiment, a userselection of the type of D.O.E. and additional D.O.E. related inputselections are received through a user interface provided in the virtualfabrication environment. Alternatively, in another embodiment, the typeof D.O.E. and D.O.E. parameters are automatically selected by thevirtual fabrication environment. A user selection of targets (e.g.:metrology measurement, a structure search, a DTC check and/or anelectrical analysis) is received (step 1504) and the analytics moduleidentifies outliers in the target data produced by the virtualfabrication runs as described above (step 1506). The identified outliersare displayed to the user and then a user selection adding one or moreof the outliers back into the target data or removing the outliers fromthe target data is received via a provided user interface (step 1508).The adjusted target data following the outlier decision is then used bythe analytics module to perform a regression analysis to identify one ormore key parameters for the D.O.E. (step 1510). An indication (e.g.list, plot, chart) of the identified key parameters is then displayed tothe user or the identified key parameters may be exported to a thirdparty application for additional processing (step 1512).

Process Model Calibration

The analytics module may also perform process model calibration. Inprocess model calibration process step parameters and settings areadjusted in the virtual fabrication environment to make the virtual 3Dmodel produced from virtual fabrication runs match a physicalsemiconductor produced in a physical fabrication environment. Oncecalibrated, the parameters and their settings in the virtualsemiconductor fabrication environment may be varied to introduce changesin the 3D models and provide insight into what process changes willimprove various semiconductor properties. In one embodiment, a wizarduser interface is provided to guide the user through the process ofoptimizing the virtual 3D model to match the physical semiconductor. Theuser selects measurement target(s) and their desired value(s), weightsthe importance of targets if there are multiple targets, sets parameterbounds, runs one or more trials, and receives optimized parameter valuesand corresponding measurement target results.

Conventional virtual fabrication environments that adjust processparameters in a calibration effort lack a system-level componentenabling proper process model calibration. Further, many semiconductorprocess integration engineers have little or no statistical knowledge.Consequently, those engineers perform process model calibration byadjusting parameters in a primitive trial and error fashion, usually viaa one-factor-at-a-time (OFAT) approach. This approach is time-consumingand gives poor quality solutions, when it finds any solution at all. TheOFAT approach guarantees that the optimal parameter sets cannot be foundbecause it does not take into account the effects of any interactionsamong the parameters.

To address these issues, embodiments provide automated statisticalanalysis, optimization, and visualization for users (e.g.: semiconductorprocess integrators who may have limited or no statistical knowledge)using an analytics module integrated into a virtual fabricationenvironment. More particularly, embodiments provide a programmaticapproach to solving the problem of calibration without confusing theengineer untrained in statistics. A statistical analysis engine in theanalytics module employs a set of analysis algorithms to analyze eachspecific use case with little user input. In one embodiment a userinterface (UI) is a wizard whose purpose is to strongly guide the userto perform the correct analysis steps. The wizard may be organized byuse cases and follow a left-side, step-wise flow UI for each use case.

An example workflow for process model calibration performed in anexemplary embodiment is depicted in FIG. 16. The sequence begins withthe virtual fabrication environment receiving an identification of adeck (layout data and process steps) from which to produce a virtual 3Dmodel of a semiconductor device of interest. In most cases the deck willbe retrieved following a user selection/specification provided via a UIprovided in the virtual fabrication environment. The UI also receives auser identification of one or more measurement targets on the 3D modelthat the user desires to have match measurement targets on acorresponding physical semiconductor (step 1602). Targets may be, butare not limited to, values related to metrology values, structuresearches, DTC checks, electrical analysis, etc. evaluated on the virtualsemiconductor structure. In another embodiment, the deck may be selectedprogrammatically without user input.

The parameters which are important (key parameters) and should beadjusted to make the 3D model target values match the experimental dataare then determined (step 2904). In one embodiment, this determinationis done via the key parameter identification process performed by theanalytics module as discussed above. Alternatively, in anotherembodiment, the key parameters may be manually selected by the user viaa UI.

The sequence continues by receiving a user specification of a desiredvalue (DV) for each target via the UI (step 1606). A DV can be, but isnot limited to, a distance obtained from a TEM, or the quality of amatch between a slice of the 3D model and a whole TEM, or an opticalspectra. Relative weighting is applied to each target by default or asindicated by the user, e.g., for two targets A and B, target A may beweighted to be twice as important as target B if the user desires.

The sequence continues by receiving a user-specification of eachparameter to be adjusted in the calibration with the user setting lowerand upper bounds (step 1608). The optimization algorithm provided in theanalytics module keeps the parameters inside these bounds as it iteratestowards a solution.

The analytics module next executes an optimization algorithm (step1610). The optimization algorithm may perform indirect or directoptimization, both of which are described further below. In oneembodiment, the user may have options to select or specify, such asnumber of iterations, convergence tolerance, type of scoring function(L−2 or L−1), number of trials, etc. In some embodiments, for multipletrials, random starting values of the parameters may be created that areinside the lower and upper bounds previously specified.

The results of the optimization algorithm are displayed to the user(step 1612). In one embodiment, the user can select a trial from thedisplayed results via the UI to trigger the building of a 3D model inthe virtual fabrication environment (step 1614).

Two different types of optimization algorithms may be used by theanalytics module. Indirect optimization applies an optimizationalgorithm to the regression equations created during the key parameteridentification process. Indirect optimization has the advantages ofbeing very fast since it does not call the virtual fabricationenvironment to build additional 3D models and generally avoids localminima because the regression equations provide a set of planes makingthe response surface (a response surface indicates the relationshipbetween the parameters and the error between the 3D model targets andDesired Values). Trials begun from random starting points in parameterspace tend to converge to similar results, so users may be able to useonly a small number of trials to perform their optimization task. Itshould also be noted that indirect optimization has the disadvantagethat if the regression equation(s) poorly predict the target(s), e.g.,if the response surface is highly non-linear, the results will be ofpoor quality.

Direct optimization is much slower than indirect optimization and may beused in an embodiment where the key parameter identification processdiscussed above is not followed. In this method, the optimizationalgorithm calls the virtual fabrication environment at each iteration,generating a new 3D model and associated metrology values and updatingthe optimization algorithm, which then adjusts the parameter values.This is a sequential optimization process. Direct optimization has theadvantages of being the most realistic method and will work better fornon-linear response surfaces, and does not necessarily require keyparameter identification process described above be run first (noregression equations are required and the user would only need to pickparameters to optimize). It has the disadvantages of being slow sincedirect optimization calls the virtual fabrication environment to build3D models at each iteration of each trial and may become trapped inlocal minima. These disadvantages can be alleviated by using multiplelicenses (speed) and more trials to provide a broader sampling ofparameter space to avoid the algorithm becoming trapped in a localminimum.

A variety of optimization algorithms can be used to perform direct andindirect optimization. As a non-limiting example, in one embodiment aninterior-point algorithm with parameter bounds may be utilized forindirect optimization, although other algorithms could be used. Fordirect optimization, as a non-limiting example, genetic algorithms maybe used as they can handle complex response surfaces withdiscontinuities and binary targets (present/absent).

As one non-limiting illustration of performing process model calibrationwith indirect optimization, in one embodiment a user first completes thekey parameter identification process via the analytics module asdescribed herein. More particularly, the user conducts an experimentaldesign and regression on a set of parameters and targets (metrology,structure search, DTC checks, electrical analysis, etc. evaluated on thevirtual semiconductor structure). This identifies the statisticallysignificant parameters for each target, and creates a regressionequation predicting each target using those statistically significantparameters. As discussed above, the user selects one or more target(s),enters the desired value (DV) for each target, and weights theirimportance. A default weighting for each target of 1 may be provided.For calibration options the user may pick if squared error is used(default) or not, and can set advanced options such as, but not limitedto, the number of optimization trials, number of iterations and theconvergence tolerance. Default values may be provided for each option.For example, the number of optimization trials may be set to a defaultvalue of 10, the number of iterations per trial may be set at a defaultvalue of 100, and the convergence tolerance may be set at a defaultvalue of 1e-6. Following the setting of the advanced options, the usermay set, via the provided UI, the allowed lower and upper bounds foreach parameter being optimized. The parameter values will be kept insidethese bounds during the optimization by the analytics module. The userinitiates the running of the calibration via the UI and the optimizationbegins. In one embodiment, the underlying compute engine may use aninterior-point algorithm. Once the optimization trial(s) complete, theoptimized parameter and target values are displayed for each trial,along with completion/error messages, and the user can select one trialto build in the virtual fabrication environment to assess the resulting3D model.

As noted above, in one embodiment, the process model calibrationsequence may be guided via a UI wizard. FIG. 17 depicts the selection ofmetrology targets for the process model calibration sequence describedabove where the user is guided to select targets from among targets forwhich regression data has been previously generated during the keyparameter identification process. As explained further below, theregression data is subsequently used when performing indirectoptimization. In one embodiment, the UI 1700 presents a selectable listof targets 1702 but limits the user to selecting from metrology targetsthat already have regression models. In an embodiment, no otherparameters and no other metrology targets are provided. FIG. 17 alsodepicts a table 1704 in the UI enabling a user to specify DVs for theselected target. In the table in the right pane the user enters DVs(those cells may initially be empty) and weights, which may be 1 bydefault and can be changed by the user.

FIG. 18 depicts an exemplary user interface 1800 enabling the selectionof calibration options 1802 which may be provided by the process modelcalibration wizard. As depicted, in one embodiment, the optimizationapproach may be selected 1804 (indirect vs. direct) and an advanceoption checkbox 1806 may be provided by the virtual fabricationenvironment to enable the user to specify options such as the number ofoptimization trials, the iterations per trial and the tolerance desiredby the user. Default values may be initially be provided which, in oneembodiment, may be changed by the user.

The process model calibration wizard may also provide a user interface1900 enabling the user to select parameter bounds as depicted in FIG.19. A list of all the statistically significant parameters in theregressions selected by the users may be created by the analytics moduleand displayed in a table format 1902. The relevant targets 1904 arelisted for each parameter. For example, in the table depicted in FIG.19, the parameter 2.1.15:thickness is significant for the threeregression targets FinCD_Top, FinCD_Bot, GapCD_Top. Users enter thedesired lower and upper bounds on each parameter.

The process model calibration wizard may then provide a run button tostart the calibration and the results may be displayed to the user via auser interface 2000 as depicted in FIG. 20. For example, the results2002 may be displayed in a table format from an internal or externalsimulation environment and may display trial number, optimizationresult, predicted target results, and values for parameters 2004. In oneembodiment, the displayed view may enable the user to select a column inthe table to export or automatically build a model in the 3D view of thevirtual fabrication environment using the parameters from a particularsuccessful trial.

Variability Analysis

Variability analysis helps the user analyze and understand thevariability in metrology data obtained for a set of virtual 3D models.In one embodiment the analytics module in the virtual fabricationenvironment can perform variability analysis to generate a userinterface that displays a table of calculated information about thetarget distribution, plots of target data histogram and normalquantiles, and provides the ability to switch to a second plot window,select up to four targets and plot/compare their empirical cumulativedistribution functions. Further, the variability analysis as describedherein provides estimates of the precision of the standard deviation(sigma) and its interrelationship with sample size, methods forassessing if target data is normally distributed, and consistent methodsfor visual comparison.

Variability analysis is a task where the user assesses the distributionof values for a target (metrology, structure search, DTC checks,electrical analysis, etc.) obtained from multiple virtual semiconductorstructures created in a virtual fabrication environment. The purpose isto determine nominal values, ranges, specification limits, etc. for thattarget. Conventional virtual fabrication environments for semiconductordevice structures lack system-level components enabling propervariability analysis. Many semiconductor process integration engineershave little or no statistical knowledge and consequently those engineersperform variability analysis in an incomplete and/or incorrect fashion.Target data may be assumed to be normally distributed, which may not bethe case, and if the target data is not normally distributed, then meanand sigma values are misleading. Even if the target data is normallydistributed, the proper sample size needed to attain useful precision ofsigma is usually not addressed in the Monte Carlosimulation/experimental design. Users frequently overestimate orunderestimate the sample size, which wastes time and/or leads to a poorquality answer. Further, visualization and comparison of distributionsare done in different software packages in different ways, or not atall, which leads to confusion among users.

To address these issues, in one embodiment the analytics module isdesigned to perform variability analysis so as to provide automatedstatistical analysis, optimization, and visualization for users (e.g.:semiconductor process integrators with limited or no statisticalknowledge) in a virtual fabrication environment.

FIG. 21 depicts a sequence of steps to perform variability analysis inan exemplary embodiment. The sequence begins with the receipt of a useridentification of a deck (layout data and process steps) used by thevirtual fabrication environment to produce a virtual 3D model of thesemiconductor device structure of interest (step 2100). The user createsa Monte Carlo D.O.E. and identifies targets for the 3D model (step2102). Multiple virtual fabrication runs are then performed for theMonte Carlo D.O.E. (step 2104). As discussed further below, in oneembodiment a reduced set of approximately 200 runs is performed. Theanalytics module identifies outliers in the target data produced by thevirtual fabrication runs in the manner described above (step 2106). Theidentified outliers are displayed to the user and a user selectionadding one or more of the outliers back into the target data or removingthe outliers from the target data for each target is received via aprovided user interface (step 2108). The user selects the variabilityanalysis option via the user interface and selects one or more targetsfor the analysis (step 2110). The variability analysis results are thendisplayed to the user in different forms, such as, but not limited to, atabular distribution data, plots of target data histogram and normalquantiles, or the results may be exported to a third party applicationfor additional processing (step 2112). If desired, the user can switchto a second plot window, an Empirical Cumulative Distribution Function(ECDF) window, and select up to four targets and the analytics modulewill plot/compare their empirical distribution functions.

FIG. 22 depicts an exemplary user interface displaying a variableanalysis results window 2200 in an exemplary embodiment. For theselected target, the variability analysis main window shows a table 2202and two plots, the histogram 2204 and the normal quantile 2206. Thetable 2202 contains multiple pieces of calculated information for theselected target: For example:

n is the number of data points used in the calculations (the user mayadd/remove outliers and therefore the actual number of data points usedis shown here);

mean and 95% CI (confidence interval) of mean;

Standard deviation and 95% confidence interval for the standarddeviation. The 95% CI is very important for the user to know, because itis an estimate of the precision of the standard deviation (sigma). Ifn=200, the 95% CI is approximately ±10%, which has been found to beuseful in estimating specification limits. A sample size of 200 is muchsmaller than is commonly recommended for Monte Carlo simulations (theusual recommendation is 10,000) but provides precision of ±10% which isacceptable for some of use cases. Users can adjust sample size (n) toimprove precision (CI) for sigma and mean as desired. In anotherembodiment, the sample size for the Monte Carlo simulation is less thanfive hundred.

Normality Test—the result of the Lilliefors Normality Test applied tothe selected target, reported as p-value and whether it is statisticallysignificant (yes/no). This is the first of multiple methods used by theanalytics module to assess whether the target data is normallydistributed;

Percentiles—min, 0.5%, 2.5%, 5%, 25%, 50% (median), 75%, 95%, 97.5%,99.5%, max for the selected target.

The variability analysis main window may also display a histogram plot,a histogram of the data for the selected target, with a normal pdfoverlaid for visual comparison of normality. If the histogram barsfollow the normal pdf, the target data can be said to be normallydistributed. This is a second method provided by the analytics modulefor testing normality of target data.

The variability analysis main window may further display a normalquantile plot of the selected target data. If the points fall close toor on the line, the target data can be said to be normally distributed.This is a third method provided by the analytics module for testingnormality of target data. It will be appreciated that additional methodsfor testing normality of target data not explicitly discussed herein mayalso be performed by the analytics module and should be considered to bewithin the scope of the present invention.

The analytics module may also generate the display of a second windowfor displaying variability analysis results. FIG. 23 depicts anexemplary user interface 2300 displaying a comparison of empiricalcumulative distribution functions of two separate targets 2302, 2304 inan exemplary embodiment. For example, the user may click on the tab 2306for the ECDF Window and select up to four targets to plot and comparetheir empirical cumulative distribution functions. The x-axis is thetarget data scaled to be in the range 0 to 1, and the y-axis is thecumulative probability from 0 to 1. This enables users to compare targetdistributions in an equivalent fashion and examine tail effects whichare important in specification limit setting.

The multiple methods for assessing normality that are made available bythe analytics module allow the user to determine whether they shouldtreat the target data as being normally distributed. If the target datais normally distributed, the user can use the mean and standarddeviation to estimate the commonly used three or four sigma points forsetting specification limits. If the data is not normally distributed,then the user may estimate useful specification limit points from thepercentiles and min/max displayed in the table, as well as from thetails of the ECDF plot. In another embodiment, the target data may beautomatically fit with Gaussian mixture models and thus used to estimateuseful points for specification limit settings. In an embodiment avariant of this approach is a feature allowing the user to fit the datawith variety of other known distributions, e.g., F or t distributions,and thereby estimate useful points for specification limit settings.

Portions or all of the embodiments of the present invention may beprovided as one or more computer-readable programs or code embodied onor in one or more non-transitory mediums. The mediums may be, but arenot limited to a hard disk, a compact disc, a digital versatile disc, aflash memory, a PROM, a RAM, a ROM, or a magnetic tape. In general, thecomputer-readable programs or code may be implemented in any computinglanguage.

Since certain changes may be made without departing from the scope ofthe present invention, it is intended that all matter contained in theabove description or shown in the accompanying drawings be interpretedas illustrative and not in a literal sense. Practitioners of the artwill realize that the sequence of steps and architectures depicted inthe figures may be altered without departing from the scope of thepresent invention and that the illustrations contained herein aresingular examples of a multitude of possible depictions of the presentinvention.

The foregoing description of example embodiments of the inventionprovides illustration and description, but is not intended to beexhaustive or to limit the invention to the precise form disclosed.Modifications and variations are possible in light of the aboveteachings or may be acquired from practice of the invention. Forexample, while a series of acts has been described, the order of theacts may be modified in other implementations consistent with theprinciples of the invention. Further, non-dependent acts may beperformed in parallel.

We claim:
 1. A non-transitory computer-readable medium holding computingdevice-executable instructions for process model calibration, theinstructions when executed causing at least one computing deviceequipped with at least one processor to: perform in a virtualfabrication environment a plurality of virtual fabrication runs for asemiconductor device based on a Design of Experiment (DOE) using 2Ddesign data and a process sequence, the plurality of virtual fabricationruns building a plurality of 3D models; receive a user identification ofone or more targets for the plurality of 3D models; receive, via a userinterface in the virtual fabrication environment, a user selection ofdesired values for selected targets associated with one or more keyparameters whose value affects measurement data for the one or moretargets; receive a user selection of upper and lower bounds for eachidentified key parameter via the user interface in the virtualfabrication environment; execute an optimization algorithm for theplurality of 3D models using the key parameters, desired values andupper and lower bounds; and display or export results from theoptimization algorithm.
 2. The medium of claim 1, wherein the keyparameters are identified in the virtual fabrication environment by ananalytics module using a regression algorithm that generates regressiondata and the optimization algorithm performs indirect optimization usingthe regression data.
 3. The medium of claim 1 wherein the key parametersare manually identified by a user and wherein the optimization algorithmperforms direct optimization.
 4. The medium of claim 1, wherein theinstructions when executed further cause the at least one computingdevice to: receive calibration options for the optimization algorithmfrom a user via the user interface.
 5. The medium of claim 4, whereinthe calibration options include one or more of a number of iterations, aconvergence tolerance, a number of trials and a type of scoringfunction.
 6. The medium of claim 1, wherein the selected targets includeat least one of a metrology measurement, a structure search, a DTC checkand an electrical analysis.
 7. The medium of claim 1, wherein relativeweighting is applied to each selected target.
 8. A computingdevice-implemented method for process model calibration, comprising:performing in a virtual fabrication environment a plurality of virtualfabrication runs for a semiconductor device based on a Design ofExperiment (DOE) using 2D design data and a process sequence, theplurality of virtual fabrication runs building a plurality of 3D models;receiving a user identification of one or more targets for the pluralityof 3D models; receiving, via a user interface in the virtual fabricationenvironment, a user selection of desired values for selected targetsassociated with one or more key parameters whose value affectsmeasurement data for the one or more targets; receiving a user selectionof upper and lower bounds for each identified key parameter via the userinterface in the virtual fabrication environment; executing anoptimization algorithm for the plurality of 3D models using the keyparameters, desired values and upper and lower bounds; and displaying orexporting results from the optimization algorithm.
 9. The method ofclaim 8, wherein the key parameters are identified in the virtualfabrication environment by an analytics module using a regressionalgorithm that generates regression data and the optimization algorithmperforms indirect optimization using the regression data.
 10. The methodof claim 8 wherein the key parameters are manually identified by a userand wherein the optimization algorithm performs direct optimization. 11.The method of claim 8, further comprising: receiving calibration optionsfor the optimization algorithm from a user via the user interfaceprovided by the virtual fabrication environment.
 12. The method of claim11, wherein the calibration options include one or more of a number ofiterations, a convergence tolerance, a number of trials and a type ofscoring function.
 13. The method of claim 8, wherein the selectedtargets include at least one of a metrology measurement, a structuresearch, a DTC check and an electrical analysis.
 14. The method of claim8, wherein relative weighting is applied to each selected target.
 15. Avirtual fabrication system, comprising: a computing device equipped witha processor and configured to generate a virtual fabricationenvironment, the virtual fabrication environment: performing a pluralityof virtual fabrication runs for a semiconductor device based on a Designof Experiment (DOE) using 2D design data and a process sequence, theplurality of virtual fabrication runs building a plurality of 3D models,receiving a user identification of one or more targets for the pluralityof 3D models, receiving, via a user interface provided by the virtualfabrication environment, a user selection of desired values for selectedtargets associated with one or more key parameters whose value affectsmeasurement data for the one or more targets, receiving a user selectionof upper and lower bounds for each identified key parameter via the userinterface, executing an optimization algorithm for the plurality of 3Dmodels using the key parameters, desired values and upper and lowerbounds, and displaying or exporting results from the optimizationalgorithm; and a display surface in communication with the computingdevice, the display surface configured to display one or more of theplurality of 3D models in a 3D view.
 16. The system of claim 15, whereinthe key parameters are identified in the virtual fabrication environmentby an analytics module using a regression algorithm that generatesregression data and the optimization algorithm performs indirectoptimization using the regression data.
 17. The system of claim 15wherein the key parameters are manually identified by a user and whereinthe optimization algorithm performs direct optimization.
 18. The systemof claim 15, wherein the virtual fabrication environment: receivescalibration options for the optimization algorithm from a user via theuser interface, the calibration options including one or more of anumber of iterations, a convergence tolerance, a number of trials and atype of scoring function.
 19. The system of claim 15, wherein theselected targets include at least one of a metrology measurement, astructure search, a DTC check and an electrical analysis.
 20. The systemof claim 15, wherein relative weighting is applied to each selectedtarget.